Two of the Washington area's major medical units - the 825-bed Washington Hospital Center and the 102,000-member Group Health Association - have asked the District government to let GHA build a new 150-bed medical center on the Hospital Center grounds.

The request is the latest step in a GHA effort to control its own hospital - and quality of care and hospital costs, according to GHA officials.

If the request is granted, the Hospital Center would provide many specialized services to GHA members. It would convert 80 of its beds to long-term rehabilitative care, a kind of care acutely needed in this area.

And the hospital Center site - bounded by Michigan Avenue, Irving and 1st Streets NW - would become a massive, 1,904-bed medical complex with four parts: the Hospital Center, the new GHA Hospital, the $58 million, 220-bed Children's Hospital, which opened in June, and the 708-bed Washington Veterans' Hospital.

Samuel Scrivener Jr., Hospital Center board chairman, said yesterday this area would benefit by having a new center of medical cooperation and "excellence."

But the District Department of Human Resources already has refused a GHA bid to build a hospital at another site. It did so on the ground that the Washington area already has too many hospital beds, and soon will have more still - including many empty ones - when new Maryland and Virginia facilities are completed.

The Hospital Center-GHA requests is in the hands of DHR director Albert P. Russo. He has the power to grant or withhold the "certificate of need" that all hospitals need to build or make major modifications.

Russo said yesterday that he and his staff must see a far more detailed presentation by GHA and the Hospital Center before he can make a decision. But he now faces not one but a series of hard decisions:

Whether to let GHA build despite the area's hospital bed surplus.

Whether a refusal on his part would seriously cripple GHA, one of the nation's largest prepaid health plans or "health maintenance organizations," a kind of medical plan being pushed by the Carter administration to help cut health costs.

What to do about another District hospital problem, the fate of downtown Doctor's Hospital. The city's Department of Human Resources has been trying to get Doctors and GHA to make some kind of cooperative agreement.

Washington Hospital Center is the creature of a series of hospital mergers that led to its present status as a huge hospital-medical office complex. It recently opened a shock-trauma unit for the severly hurt, and is classed with the major university centers - Georgetown, George Washington and Howard - among the area's medical leaders.

GHA is one of the nation's pioneer prepaid health plans. But it has been suffering from high health costs, and last year it transferred most of its hospital care from George Washington to Doctors Hospital to avoid the highly daily rates of a university center.

Doctors Hospital, a 40-year-old facility in the 1800 block of I Street NW, has been seeking to build its own new facility. Its building is slated for demolition by 1980 to make way for the final section of the International Square office-retail complex.

Doctor's parent corporation, Washington Medical Center (WMC), first sought to put up a new hospital on 20th Street NW between I and K. But WMC could not get financing there and sold the property.

WMC then proposed a downtown 19th Street site owned by a firm controlled by developer Dominic F. Antonelli Jr. Former DHR Director Joseph Yeldell twice extended WMC's certificate to build a new hospital despite his health planners' advice that the beds were unneeded.

Last year it was disclosed that Antonelli as an officer of the hospital had negotiated with Yeldell at the same time Yeldell was getting $54,000 in personal loans with Antonelli's help.

Now Doctors Hospital has another plan altogether: to convert its Metropolitan Hotel property at 1143 New Hampshire Ave NW, originally built as a chronic care hospital, into an acute-care hospital at what WMC officers call a "bargain" figure.

"We could do this for $15 or $16 million," George Kell, WMC vice president, said yesterday. "We'd have 250 acute beds, and with 42 beds there already being used by the Psychiatric Institute of Washington, the District would have nearly a 300-bed facility at very reasonable cost."

Doctors Hospital physicians and the D.C. Medical Society both argue that, no matter what GHA does, Doctors should be allowed to use the Metropolitan site to keep physicians in downtown Washington instead of the suburbs.

Russo since May has again twice extended the Doctors Hospital building certificate to give WMC time to try to negotiate with GHA on long-term sharing and to give his own staff time to deliberate. He said he will announce a final decision on the Doctors certificate Wednesday.

GHA and Doctors officials last met early this month but still reached no agreement.

Neither GHA's nor the Washington Hospital Center's board has finally approved their proposed agreement, which would see GHA leasing some Hospital Center land.

But a GHA "progress report" last week said consultants's studies have found the Doctors-Metropolitan site "undesirable" for the GHA, while a hospital site at the Hospital Center could give the nation a "model" health maintenance organization.